Programs

Signals and Stochastic Processes

In typical applications of science and engineering, we have to processsignals, using systems. While the applications can be varied large communication systems to control systems but the basic analysis and design tools are the same. In a signals and systems course, we study these tools: convolution,Fourier analysis, z-transform, and Laplace transform. The use of thesetools in the analysis of linear time-invariant (LTI) systems with deterministic signals. For most practical systems, input and output signals are continuous and these signals can be processed using continuous systems. However,due to advances in digital systems technology and numerical algorithms,it is dvantageous to process continuous signals using digital systems byconverting the input signal into a digital signal. Therefore, the study of both continuous and digital systems is required.As most practical systems are digital and the concepts are relativelyeasier to understand, we describe discrete signals and systems _rst, immediately followed by the corresponding description of continuous signalsand systems

Properties of continuous Fourier Tranform :These properties provides significant amount of insight into the transform and into the relationship between the time-domain and frequency domain descriptions of a signal. Many of these properties are useful in reducing the complexity Fourier transforms or inverse transforms. By using these properties we can translate many Fourier transform properties into the corresponding Fourier series properties

To analyze the characteristics of a random signal in time domain, one need to estimate certain parameters like Mean, Variance, correlation etc. This particular module deals with Autocorrelation, Cross Correlation, Covariance and its properties. These parameters play a vital role in signal estimation and analysis in various applications like RADR, SONAR, and NAVY etc.

Analysis of LTI System Response :This particular module discusses the methods of describing the out response of a linear time invariant system (LTI) when a continuous random process is applied at the input

Random Processes – Spectral Characteristics : To design any LTI filter which is intended to extract or suppress the signal, it is necessary to understand how the strength of a signal is distributed in the frequency domain, relative to the strengths of other ambient signals. Similar to the deterministic signals, it turns out to be just as true in the case of random signals

Spectral characteristics of system response :The quality of a communication system deals with the delivery of message to the user, who is available after the receiver. The present module deals with the effect of an LTI system on the input random process. This in turn helps in the computation of S/N at the output of thr receiver in a communication system

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